An Exotic Deformation of the Hyperbolic Space

Let Isom(H^n) be the group of isometries of the n-dimensional real hyperbolic space. We first classify all continuous non-elementary actions of on the infinite-dimensional real hyperbolic space. We then prove the existence of a continuous family of non-isometric minimal proper CAT(-1) spaces on which Isom(H^n) acts cocompactly by isometries.